IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v67y2009i1p277-291.html
   My bibliography  Save this article

The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments

Author

Listed:
  • Fong, Yuk-fai
  • Surti, Jay

Abstract

In the infinitely repeated Prisoners' Dilemma with side payments, we characterize the Pareto frontier of the set of subgame perfect equilibrium payoffs for all possible combinations of discount factors. Play paths implementing Pareto dominant equilibrium payoffs are uniquely determined in all but the first period. Full cooperation does not necessarily implement these payoffs even when it maximizes total stage game payoffs. Rather, when the difference in players' discount factors is sufficiently large, Pareto dominant equilibrium payoffs are implemented by partial cooperation supported by repeated payments from the impatient to the patient player. When both players are sufficiently patient, such payoffs, while implemented via full cooperation, are supported by repeated payments from the impatient to the patient player. We characterize conditions under which public randomization has no impact on the Pareto dominant equilibrium payoffs and conditions under which such payoffs are robust to renegotiation.

Suggested Citation

  • Fong, Yuk-fai & Surti, Jay, 2009. "The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments," Games and Economic Behavior, Elsevier, vol. 67(1), pages 277-291, September.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:277-291
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00206-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    2. Andreoni,J. & Varian,H., 1999. "Pre-play contracting in the prisoners' dilemma," Working papers 18, Wisconsin Madison - Social Systems.
    3. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    4. Carmichael, H Lorne & MacLeod, W Bentley, 1997. "Gift Giving and the Evolution of Cooperation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 485-509, August.
    5. van Damme, Eric, 1989. "Renegotiation-proof equilibria in repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 47(1), pages 206-217, February.
    6. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    7. Farrell, Joseph & Maskin, Eric, 1989. "Renegotiation in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 327-360, December.
    8. Matthew O. Jackson & Simon Wilkie, 2005. "Endogenous Games and Mechanisms: Side Payments Among Players," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 543-566.
    9. Marco Celentani & Drew Fudenberg & David K. Levine & Wolfgang Pesendorfer, 2008. "Maintaining A Reputation Against A Long-Lived Opponent," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 9, pages 163-176, World Scientific Publishing Co. Pte. Ltd..
    10. Mailath, George J. & Obara, Ichiro & Sekiguchi, Tadashi, 2002. "The Maximum Efficient Equilibrium Payoff in the Repeated Prisoners' Dilemma," Games and Economic Behavior, Elsevier, vol. 40(1), pages 99-122, July.
    11. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107, Elsevier.
    12. Evans, Robert & Maskin, Eric, 1989. "Efficient renegotiation--proof equilibria in repeated games," Games and Economic Behavior, Elsevier, vol. 1(4), pages 361-369, December.
    13. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    14. Baliga, Sandeep & Evans, Robert, 2000. "Renegotiation in Repeated Games with Side-Payments," Games and Economic Behavior, Elsevier, vol. 33(2), pages 159-176, November.
    15. Friedel Bolle, 2001. "Why to Buy Your Darling Flowers: On Cooperation and Exploitation," Theory and Decision, Springer, vol. 50(1), pages 1-28, February.
    16. Ehud Lehrer & Leeat Yariv, 1999. "Repeated Games with Incomplete Information on One Side: The Case of Different Discount Factors," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 204-218, February.
    17. Barrett, Scott, 2001. "International cooperation for sale," European Economic Review, Elsevier, vol. 45(10), pages 1835-1850, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
    2. Carmona, Guilherme & Carvalho, Luís, 2016. "Repeated two-person zero-sum games with unequal discounting and private monitoring," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 131-138.
    3. Malcolm Kass & Enrique Fatas & Catherine Eckel & Daniel Arce, 2015. "The UN in the lab," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(3), pages 625-651, October.
    4. Roman, Mihai Daniel, 2008. "Entreprises behavior in cooperative and punishment‘s repeated negotiations," MPRA Paper 37527, University Library of Munich, Germany, revised 05 Jan 2009.
    5. Heidi Gjertsen & Theodore Groves & David A Miller & Eduard Niesten & Dale Squires & Joel Watson, 2021. "Conservation Agreements: Relational Contracts with Endogenous Monitoring," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 37(1), pages 1-40.
    6. David A. Miller & Joel Watson, 2013. "A Theory of Disagreement in Repeated Games With Bargaining," Econometrica, Econometric Society, vol. 81(6), pages 2303-2350, November.
    7. Susanne Goldlücke & Sebastian Kranz, 2018. "Discounted stochastic games with voluntary transfers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 235-263, July.
    8. Do, Jihwan, 2022. "Cheating and compensation in price-fixing cartels," Journal of Economic Theory, Elsevier, vol. 200(C).
    9. Suzi Kerr & Steffen Lippert & Edmund Lou, 2019. "Financial Transfers and Climate Cooperation," Working Papers 19_04, Motu Economic and Public Policy Research.
    10. Heidi Gjertsen & Theodore Groves & David A. Miller & Eduard Niesten & Dale Squires & Joel Watson, 2014. "A Contract-theoretic Model of Conservation Agreements," World Scientific Book Chapters, in: Kaddour Hadri & William Mikhail (ed.), Econometric Methods and Their Applications in Finance, Macro and Related Fields, chapter 15, pages 425-455, World Scientific Publishing Co. Pte. Ltd..
    11. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
    12. Kranz, Sebastian & Ohlendorf, Susanne, 2009. "Renegotiation-Proof Relational Contracts with Side Payments," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 259, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    13. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haag, Matthew & Lagunoff, Roger, 2007. "On the size and structure of group cooperation," Journal of Economic Theory, Elsevier, vol. 135(1), pages 68-89, July.
    2. Goldlücke, Susanne & Kranz, Sebastian, 2013. "Renegotiation-proof relational contracts," Games and Economic Behavior, Elsevier, vol. 80(C), pages 157-178.
    3. W. Bentley MacLeod & James M. Malcomson, 2023. "Implicit Contracts, Incentive Compatibility, and Involuntary Unemployment: Thirty Years On," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 179(3-4), pages 470-499.
    4. W. Bentley MacLeod, 2006. "Reputations, Relationships and the Enforcement of Incomplete Contracts," CESifo Working Paper Series 1730, CESifo.
    5. Leif Helland & Jon Hovi, 2008. "Renegotiation Proofness and Climate Agreements: Some Experimental Evidence," Nordic Journal of Political Economy, Nordic Journal of Political Economy, vol. 34, pages 1-2.
    6. Matthias Blonski & Giancarlo Spagnolo, 2015. "Prisoners’ other Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 61-81, February.
    7. Aramendia, Miguel & Wen, Quan, 2020. "Myopic perception in repeated games," Games and Economic Behavior, Elsevier, vol. 119(C), pages 1-14.
    8. Conconi, Paola & Perroni, Carlo, 2009. "Do credible domestic institutions promote credible international agreements?," Journal of International Economics, Elsevier, vol. 79(1), pages 160-170, September.
    9. Stähler, Frank, 1995. "Profits in pure Bertrand oligopolies," Kiel Working Papers 703, Kiel Institute for the World Economy (IfW Kiel).
    10. Yuval Heller & Christoph Kuzmics, 2019. "Renegotiation and Coordination with Private Values," Graz Economics Papers 2019-10, University of Graz, Department of Economics.
    11. Perroni, Carlo & Scharf, Kimberley, 2003. "Viable Tax Constitutions," The Warwick Economics Research Paper Series (TWERPS) 683, University of Warwick, Department of Economics.
    12. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
    13. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    14. Ely, Jeffrey & Fudenberg, Drew & Levine, David K., 2008. "When is reputation bad?," Games and Economic Behavior, Elsevier, vol. 63(2), pages 498-526, July.
    15. Aramendia, Miguel & Wen, Quan, 2014. "Justifiable punishments in repeated games," Games and Economic Behavior, Elsevier, vol. 88(C), pages 16-28.
    16. Buchholz Wolfgang & Heindl Peter, 2015. "Ökonomische Herausforderungen des Klimawandels," Perspektiven der Wirtschaftspolitik, De Gruyter, vol. 16(4), pages 324-350, December.
    17. Waknis, Parag, 2017. "Competitive Supply of Money in a New Monetarist Model," MPRA Paper 75401, University Library of Munich, Germany.
    18. Dasgupta, Ani & Ghosh, Sambuddha, 2022. "Self-accessibility and repeated games with asymmetric discounting," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. James M. Malcomson, 2012. "Relational Incentive Contracts [The Handbook of Organizational Economics]," Introductory Chapters,, Princeton University Press.
    20. McCutcheon, Barbara, 1997. "Do Meetings in Smoke-Filled Rooms Facilitate Collusion?," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 330-350, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:277-291. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.